Constrained Bias Correction (CBC) For Satellite Radiance Assimilation
Wei Han
NWPC/CMA
ITSC19, March 27, 2014
Outline
• Background
– The bias correction is an ill‐posed problem
– Two Remain Issues of bias correction
– Efforts has been done
• Methodology
J 
J
, y  Hxb  b
y
FSO: Forecast sensitivity to observation
Over or under bias correction could lead to negative impact
– Use of priori information as constraint: Constrained BC (CBC)
– Implementation in VarBC
– Implementation in offline BC
• Experiments of CBC in GRAPES
– Consideration of imperfect QC: AMSUA Ch4
– Consideration of imperfect model: AMSUA Ch9
– Impact on forecasts
• Discussions and Further Plan
Background
• The bias correction is an ill-posed problem: O-B?
– There is no absolute calibration of satellite instruments on orbit
– There is no truth of the atmosphere
– How to separate observation bias from model bias using O‐B?
• Two main issues
– Imperfect QC affacted BC: QC and BC interaction
• Window channel: cloud contamination
– Model bias
• Temperature sounding channel in stratosphere
• Trace gas sounding channel, e.g. IASI Ozone channels
• Developing models : GRAPES
Background‐‐Efforts been done for QC feedback
• Imperfect QC
– Warm tail for microwave window channel departures O‐B
– Cold tail for IR window channel departures O‐B
– Over correction on observations by Least Square based estimation
• Using mode
– Han and McNally 2008
– Li ,McNally and Geer,2010
J ( m) 
1 n
 (di  m)2 [ p(di )]
2n 1
Han and McNally,2008
Mean Based 2007D08JF,ECMWF,IFS
Impact of over bias correction Mean: If bias is estimated by <O-B>, It will
strongly depend on the QC,
0.7  b=0.4; 0.1  b=0.28
Mode Based
METOP AMSUA CH4
f0xx_2008011200
Low cloud cover
Background‐‐Efforts been done for model error
• Using “UNBIASED” observations
– Radiosonde mask (Eyre 1992)
– Radiosonde profile (Joiner and Rokke 2000;Kozo et al.,2005)
– GPS RO temperature sounding (Zou et al.,2014)
• VarBC using all other un-corrected observations
– Derber and Wu 1998; Dee 2004; Auligne et al.2007
• Anchor channel
– AMSUA Ch14 (McNally,2007)
– IASI ozone channel (Han and McNally,2010)
• Bias model selection: Constrain the freedom of bias predictor
– Freedom of the predictor
– Absorption correction (Watts and McNally 2004)
– Frequency correction (Lu et al.,2011)
How to separate
observation bias
from O-B?
Courtesy of Fiona Hilton,ITSC16
Radiance priori information: bias and uncertainty
Han and McNally,2010
Connection between BC and Calibration
•
Account for the calibration uncertainty in BC
Courtesy of Yong Han,2014,ITSC19
Methodology
1
x
2J (x, β)  (xb  x) B (xb  x)
T
  b (β  βb )T B1 (β  βb )
1
 [y  H (x)  h(x, β)] R [y  H (x)  h(x, β)]
T
  [h(x, β)  b0 ]T Rb1[h(x, β)  b0 ]

: Regularization parameter
b
0
 0
Use of PRIORI information
Radiometric Uncertainty
RT model Uncertainty
: Priori estimate of observation bias
R :b Priori estimate uncertainty
β
B
b
: Background predictor coefficients
 : Background predictor coefficients uncertainty
Adaptive
Constrained Bias Correction (CBC) scheme
2 J (x, β)  (xb  x)T B x 1 (xb  x)
d  y  H ( x)
  b (β  βb )T B 1 (β  βb )
 [y  H (x)  h(x, β)] T R 1 [y  H (x)  h(x, β)]
Pβ  h(x, β)
  [h(x, β)  b0 ]T R b1[h(x, β)  b 0 ]
β J (x, β)
  b B 1 (β  βb )  PT R 1 [d  Pβ]   PT R b1[Pβ  b 0 ]
 ( b B 1  PT R 1P   PT R b1P )β  ( b B 1 βb  PT R 1d   PT R b1b 0 )
β J (x, β)  0　
Aβ  z
A   b B 1  PT R 1P   PT R b1P
z   b B 1 βb  PT R 1d   PT R b1b 0
VarBC, Regression BC and Constrained BC(CBC)
A   bB1  PT R1P   PT Rb1P
Aβ  z
z   bB1 βb  PT R1d   PT Rb1b0
 b  0,   0, R  I

 b  1,   0

Pβ  d
Linear Regression BC
β J (x, β)   bB1 (β  βb )  PT R1 [d  Pβ] VarBC
For the simplest example, with a global constant as predictor:
P  1, β   0 , R  R b  1

1
0 
1 
N
 (d   b )
i 1
0 i
Experiments of CBC in GRAPES
Model bias
Ch9
Warm tail
Ch4
  0, b0  0
  1, b0  0.3(mod e)
<O-B>CBC
Warm tail
<O-B>ori BC
AMSUA CH4(Metop_A)
Model Bias
<b1-b0>
1-10 June 2013
  0, b0  0
  1, b0  0
<O-B>ori BC
AMSUA CH9(Metop_A)
<O-B>CBC
Model Bias
<b1-b0>
Two months cycle experiments in GRAPES global
May‐June 2013
Impact on Analysis: <T_grapes‐T_ncep> ,20S‐20N
INT
INTCBC
N.H.
S.H.
Zonal Wind
N.H.
S.H.
Geo. Height
Impact of CBC on forecasts 60 cases, May 1 – June 30 ,2013
Impact of CBC on forecasts
• Positive Impact
Wind RMS
Global Mean
Discussions and Further Plan
• Implementation of Constrained Bias Correction (CBC) scheme – VarBC – offline regression BC
• Capabilities of CBC
– Considering imperfect QC
– Considering model bias
• important for developing models
• Important for trace gases
• Estimation and Tuning of the Priori Parameters
–
–
–
–
Using mode as priori bias estimate
Using other unbiased obs. to get Radiometric calibration uncertainty
RT model uncertainty